Subgroups — #3874⋊D₄₉ #28412939

Order 14700.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20301201	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₉⋊#3874	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₉×#3874	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×D₂₄₅	—	3	1	no	maximal, Hall
5	C₄₉×C₅²⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₅⋊D₂₄₅	D₃	1	1	yes	characteristic, complemented
7	C₅×D₂₄₅	—	3	1	no	—
8	C₅×D₅×C₄₉	—	3	1	no	—
9	#3874⋊D₇	—	7	1	no	maximal
10	C₅²×C₄₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	#11760384	—	7	1	no	—
12	C₇⋊#3874	—	7	1	no	—
13	C₇×#3874	D₇	1	1	yes	characteristic
14	C₂×D₂₄₅	—	15	1	no	—
15	D₅×D₄₉	—	15	1	no	—
16	D₅×D₃₅	—	21	1	no	—
17	D₃×D₄₉	—	25	1	no	maximal, Hall
18	C₇×C₅²⋊C₃	C₂×D₇	1	1	yes	characteristic
19	C₂×C₅×C₄₉	—	15	1	no	—
20	D₂₄₅	—	3	1	no	—
21	D₂₄₅	—	15	1	no	—
22	D₂₄₅	—	15	1	no	—
23	C₅×D₄₉	—	15	1	no	—
24	D₅×C₄₉	—	3	1	no	—
25	C₅⋊D₃₅	—	7	1	no	—
26	C₅×D₃₅	—	21	1	no	—
27	C₅×C₇×D₅	—	3	1	no	—
28	#3874⋊C₂	—	49	1	no	Hall
29	D₁₄₇	—	25	1	no	—
30	C₃×D₄₉	—	25	1	no	—
31	D₃×C₄₉	—	25	1	no	—
32	C₅×C₄₉	—	3	1	no	—
33	C₅×C₄₉	—	3	1	no	—
34	C₂×D₄₉	—	75	1	no	Hall
35	C₅²×C₇	D₃×D₇	1	1	yes	characteristic
36	(C₅⋊D₅)⋊C₃	—	49	1	no	—
37	#3874	—	49	1	no	—
38	#3874	D₄₉	1	1	yes	characteristic, complemented
39	C₃×C₄₉	—	25	1	no	Hall
40	C₂×D₃₅	—	105	1	no	—
41	D₅×D₇	—	105	1	no	—
42	D₅²	—	147	1	no	Hall
43	C₂×C₄₉	—	15	1	no	—
44	D₄₉	—	15	1	no	—
45	D₄₉	—	25	1	no	—
46	D₃×D₇	—	175	1	no	—
47	C₅²⋊C₃	C₂×D₄₉	1	1	yes	characteristic, complemented, Hall
48	C₂×C₅×C₇	—	15	1	no	—
49	D₃₅	—	21	1	no	—
50	D₃₅	—	105	1	no	—
51	D₃₅	—	105	1	no	—
52	C₅×D₇	—	105	1	no	—
53	C₇×D₅	—	3	1	no	—
54	C₅⋊D₅	—	49	1	no	—
55	C₅×D₅	—	3	1	no	—
56	C₅×D₅	—	147	1	no	—
57	C₄₉	#3874⋊C₂	1	1	yes	characteristic, complemented, Sylow
58	D₂₁	—	175	1	no	—
59	C₃×D₇	—	175	1	no	—
60	D₃×C₇	—	25	1	no	—
61	C₅×C₇	—	3	1	no	—
62	C₅×C₇	—	3	1	no	—
63	C₂×D₇	—	525	1	no	—
64	C₅²	D₃×D₄₉	1	1	yes	characteristic, complemented, Sylow
65	C₃×C₇	—	25	1	no	—
66	C₂×D₅	—	735	1	no	—
67	C₂×D₅	—	735	1	no	—
68	C₂×C₇	—	15	1	no	—
69	D₇	—	105	1	no	—
70	D₇	—	175	1	no	—
71	C₂×D₃	—	1225	1	no	Hall
72	C₂×C₅	—	15	1	no	—
73	C₂×C₅	—	735	1	no	—
74	D₅	—	3	1	no	—
75	D₅	—	147	1	no	—
76	D₅	—	735	1	no	—
77	D₅	—	735	1	no	—
78	C₇	#3874⋊D₇	1	1	yes	characteristic
79	C₂×C₃	—	1225	1	no	—
80	D₃	—	25	1	no	—
81	D₃	—	1225	1	no	—
82	C₅	—	3	1	no	—
83	C₅	—	3	1	no	—
84	C₂²	—	3675	1	no	Sylow
85	C₃	—	25	1	no	Sylow
86	C₂	—	15	1	no	—
87	C₂	—	1225	1	no	—
88	C₂	—	735	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₄₉×C₅²⋊C₃	C₂²
Frattini	C₇	#3874⋊D₇
Fitting	C₅²×C₄₉	C₂×D₃
socle	C₅²×C₇	D₃×D₇
LCS	G ▷ C₄₉×C₅²⋊C₃
UCS	C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #20301201	C₂	semidirect
2. C₄₉⋊#3874	C₂	semidirect
3. C₄₉×#3874	C₂	semidirect
5. C₄₉×C₅²⋊C₃	C₂²	semidirect
6. C₅⋊D₂₄₅	D₃	semidirect
10. C₅²×C₄₉	C₂×D₃	semidirect
38. #3874	D₄₉	semidirect
47. C₅²⋊C₃	C₂×D₄₉	semidirect
57. C₄₉	#3874⋊C₂	semidirect
64. C₅²	D₃×D₄₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#20301201	2
C₄₉⋊#3874	2
C₄₉×#3874	2
D₅×D₂₄₅	3
#3874⋊D₇	7
D₃×D₄₉	25

Subgroups — #3874⋊D49 #28412939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3874⋊D₄₉ #28412939